Simplify to lowest terms. $\dfrac{42}{63}$
There are several ways to tackle this problem. What is the greatest common factor (GCD) of 42 and 63? $42 = 2\cdot3\cdot7$ $63 = 3\cdot3\cdot7$ $\mbox{GCD}(42, 63) = 3\cdot7 = 21$ $\dfrac{42}{63} = \dfrac{2 \cdot 21}{ 3\cdot 21}$ $\hphantom{\dfrac{42}{63}} = \dfrac{2}{3} \cdot \dfrac{21}{21}$ $\hphantom{\dfrac{42}{63}} = \dfrac{2}{3} \cdot 1$ $\hphantom{\dfrac{42}{63}} = \dfrac{2}{3}$ You can also solve this problem by repeatedly breaking the numerator and denominator into common factors. For example: $\dfrac{42}{63}= \dfrac{3\cdot14}{3\cdot21}= \dfrac{3\cdot 7\cdot2}{3\cdot 7\cdot3}= \dfrac{2}{3}$